1. Introduction

Generating secondary sources of radiation during filamentation is an important application of femtosecond lasers, in particular for the generation of ultrashort tunable pulse and the teledetection of atmospheric pollutants [1]. The effects of self-focusing, diffraction and plasma self-defocusing are counterbalanced so the pulse can propagate over an extended region of high intensity, thus enhancing the nonlinear processes occurring in the filamenting zone. Sources of radiation in the ultraviolet [2], visible [3], infrared [4–6], and up to the terahertz region [7,8], have been developed using different conditions for filamentation. In particular, it has been shown that four-wave mixing between two pulses of slightly different wavelengths is a proper way to generate a tunable infrared source [9]. In this scheme, the laser beam is split in two arms using a configuration similar to a Michelson interferometer. One pulse is frequency doubled in the first arm and the second harmonic is recombined with the fundamental pulse of the second arm in a filament where the parametric interaction of these two-color laser pulses generates infrared (IR) radiation through the χ⁽³⁾ nonlinear response of the medium. However, the IR fluctuation due to the unavoidable mechanical vibration is serious for the two-arm scheme especially for long distance experiments. In this paper, we propose a new in-line method consisting of shaping the laser emission spectrum in order to use a single beam to remotely produce tunable broadband IR pulse.

2. Spectral Shaping of the Femtosecond Laser

The experiments presented here have been performed at the Advanced Laser Light Source (ALLS) Canadian facility. The laser system was a 10 Hz titanium sapphire laser delivering femtosecond pulses having tens of milliJoules of energy. The key element in shaping the spectrum of the femtosecond laser beam was the AOPDF. Briefly, this device is a crystal which diffracts the incident laser beam as it is excited by an acoustic wave. By using a radio frequency (RF) synthesizer, it can be viewed as a filter with programmable transfer function in the spectral domain [10]. Two AOPDFs were inserted in the Ti:Sapphire laser used for the experiment. The first AOPDF was placed after the stretcher and was used to compensate for the dispersion through the laser chain in order to get the shortest pulse out of the compressor. The second was placed inside the regenerative amplifier and was used to struggle against gain narrowing by partially rejecting the central part of the spectrum for every pass in the regenerative cavity, favoring amplification of the wings and resulting in a constant spectral gain. This configuration allowed an amplified spectrum extending from 750 nm to 840 nm [11], being limited by the stretcher gratings size and the mirrors reflectivity.

In our experiment, we applied an equivalent amplitude filter to divide the oscillator spectrum into two distinctive spectra corresponding to two copropagating pulses with different wavelengths. This was done by superposition of two RF signals in the first AOPDF crystal. The method allowed controlling independently each spectrum amplitude and phase and also the relative delay between the pulses by delaying the RF signals. When the spectrum was split, the laser pulse having a central wavelength lower than 800nm was named “red pulse” and the other one having a central wavelength longer than 800nm was named “NIR pulse”. In this experiment, the phase was kept linear so both laser pulses remained unchirped and only the delay was varied. Figure 1(a) ) shows the setup for filamentation with different configurations programmed for the laser (Fig. 1(b), 1(d) and 1(f)).

 

Fig. 1 (a) Optical lay-out used for in-line two-color filamentation, Three different spectral shape generated by the laser system and explored during the experiment (b,d,f). The blue and red laser pulses spectra after all the optical components of the in-line setup (c,e,g).

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3. Filamentation in Air and Four-Wave Mixing

We now describe in details the experimental conditions under which we could produce IR radiation by the spectral shaping method. The laser beam diameter was reduced from 100mm to 25mm with an iris in order to decrease the numerical aperture of the lens to ~1/500. Adjusting the numerical aperture had the effect of generating relatively long filament zone (60 cm) instead of creating strong plasma close to the geometrical focus, which would not have been representative for long range filamentation in air. Then, a 0.4mm thick type-1 KDP crystal was used and its crystal-axis angle was adjusted in order to frequency-doubled only the NIR pulse. Since the second-harmonic (SH) pulse had an orthogonal polarization, an 800 nm half-wave plate (λ/2) was inserted to rotate the fundamental polarization without significantly affecting the second harmonic polarization. Furthermore, a dichroic mirror (DM) was necessary to filter out the remaining NIR pulse in order to avoid the NIR pulse to create a filament that would had diffracted the two pulses of interest (red and SHG) that propagate slower in the optical components. The resulting spectra that were finally used for filamentation are shown in Fig. 1(c), 1(e) and 1(g). The total energy, considering both red and second harmonic pulses in each configuration, was adjusted to 10 mJ measured after the lens. All the experiments were performed in air.

A SiO₂ lens was used instead of a focusing mirror in order to maximize the longitudinal overlap of the interaction zone between the SH pulse and the self-focusing red pulse; due to chromatic aberration, the geometrical focus of the lower energy SH pulse was shorter which compensated for the self-focusing of the red pulse which formed its filament prior the geometrical focus. The temporal overlap of the two pulses could furthermore be actively optimized using the AOPDF.

The visible part of the supercontinuum generated after the filament was measured using an integration sphere and fiber coupled spectrometers (Ocean Optics, QE65000, HR4000 & NIR512). For measuring the IR supercontinuum, a silicon wafer was inserted after the filament to filter out the part of the generated spectrum below 1 μm and a 15 cm diameter NaCl lens (60cm focal length) was used to collect the remaining supercontinuum and focus it on the entrance slit of the NaCl prism monochromator. The NaCl lens was large enough to collect the whole IR supercontinuum generated from the filaments. The signal at the output of the monochromator was measured by two different IR detectors detailed in [5], to cover a bandwidth ranging from 1 μm to 13 μm. Spectral overlap between the measurements of the fiber spectrometers and the monochromator insured continuity of the measured spectra shown in Fig. 2 .

 

Fig. 2 Broadband spectra resulting from the two-color filamentation of the three different spectral shapes obtained in Fig. 1(c), 1(e) and 1(g). In each case, the delay between the two pulses was adjusted to maximize the infrared signal.

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According to the conservation of energy during four-wave-mixing (FWM), the generated IR frequency (ω_IR) in each laser spectral shape configuration can be calculated as where two red photons (ω_red) mix with a blue photon (ω_SH). In order to adjust the delay between pulses, we set the monochromator for the expected IR wavelength and adjusted the delay to maximize the IR signal. IR signal was only observed within a inter pulses delay window of 200 fs, which confirmed that the IR was generated by the overlap of the two 100 fs pulses. We verified the signal at different wavelengths to ensure that the optimum delay is the same for any IR wavelength and that the spectrum is not shifted when changing the delay. To further confirm that the IR signal was generated by the overlap of the two pulses, we inserted a 1mm microscope slide (corning 0215) just before the filament and observed an IR signal drop which can be completely retrieved by changing the delay by about 120 fs, corresponding to the approximate delay introduced between SH and red pulses in the glass plate. In comparison, inserting a sapphire plate just after the filament zone has no effect on the detected signal except for the Fresnel losses. This observation demonstrates that the IR generation takes place within the filament zone, which extends over 60 cm.

In the first laser beam configuration using a single NIR pulse (Fig. 1(c)), it was not possible to actively control the delay between the 818 nm and 409 nm pulses with the AOPDF and both pulses did not interact inside the filament due to dispersion in optics materials. In fact, the NIR pulse was always in front of the blue one, and thus, as shown in Fig. 2, we observed an extension in the IR supercontinuum similar to that reported for the propagation of a single femtosecond pulse in the atmosphere [6]. In the cases where the laser beam was spectrally shaped to form two pulses, the inter pulse delays were actively adjusted with the AOPDF and we observed a tremendous increase of the IR generation. By mixing the 771 nm and 417 nm pulses (Fig. 1(g)), the signal detected around 4 µm was at least three orders of magnitude more important than for the single NIR pulse. The expected central wavelength generated by mixing the 771 nm and 417 nm pulse is around 5.1 μm, which differs from the measured peak wavelength around 4 μm (Fig. 2). The blue-shift of the generated IR pulse is directly related to the blue-shift of the pump pulses occurring during the filamentation [9,12–14]. In the case of mixing the 791 nm and 412 nm pulses (Fig. 1(e)), the expected IR peak signal is around 9.9 μm and the measured spectrum extends in the far IR up to 12 μm with a sustained signal between 7 and 10 μm that is five orders of magnitude more important than that reported for a single pulse configuration in [6].

The angular IR emission generated by the mixing of the 791 nm and 412 nm pulses was characterized in the far-field by moving a HgCdTe detector with different IR bandpass filters across the beam profile. We observed IR conical emission as it is shown in Fig. 3(a) . The divergence of the IR conical emission (CE) with the two-pulse configuration was 2-3 times lower than for the IR CE from a single NIR pulse [6]. Based on the phase-matching condition for FWM, the decrease of the IR divergence in the current experiment is due to the use of lower divergence SHG pulses in the filament zone, which was not the case for the single color filament where the IR signal originate from the FWM between the fundamental NIR pulse (on propagation axis) and its blue conical emission [6]. To compare this measured IR CE with the calculated off-axis phase matching inside the filament, we considered a collimated red pulse (plane wavefront in the filament) and a spread of wavevectors within ± 2 mrad relative to the propagation axis for the blue pulse (due to initial focusing). According to the linear refractive index in air [15], a perfect phase-matching is achieved at a certain divergence for a given IR wavelength (see black line in Fig. 3(b)). The calculated off-axis phase matching corresponds well with the measured IR CE, indicating here that the Kerr nonlinear refractive index change does not significantly affect the phase-matching condition.

 

Fig. 3 (a) Measured spatial distribution for different IR wavelengths in the case of the 791nm-412nm four-wave mixing and (b) divergence expected from phase-matching calculations in comparison with the experimental results. The grey zone in (b) corresponds to the off-axis phase-matching angle for the ±2 mrad initial divergence of the blue pulse.

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4. Conclusion

In conclusion, we demonstrated the IR generation by two-color filamentation in an in-line setup by spectrally shaping a femtosecond laser beam. We measured the spectral emission for different double-pulse configurations which can be actively controlled by changing the AOPDF parameters that shape the spectrum. The separation of the spectral maximum peaks determine the IR emission; mid-IR can be generated with a large separation while reducing the spectral separation generates IR emission extending in the far IR up to 12 μm. We also measured the characteristic divergence of the IR CE which is in agreement with the off-axis phase-matching conditions during FWM. The amplification of two pulses by modulation of the spectral amplitude and phase is a simple method that enables to perform two-color filamentation with a single beam. It gives the ability to finely control the pulse delay and skillfully achieve spatial and temporal overlap in the filament without separation and recombination of the laser beam. This technique is promising for any pump-probe experiments or remote parametric generation for long range applications.